{
 "metadata": {
  "name": "",
  "signature": "sha256:be1cda8f4268f225b6545611eed896bf8be14811029f28365ad5135e8d4c9259"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<h2>Marginal Likelihood for model selection</h2>\n",
      "<p>In this notebook we will look at using marginal likelihood as a quantity for model selection. We will generate data from a 3rd order polynomial, and then fit models from 1st to 8th order. For each model, we'll compute the posterior density over model parameters and also compute the marginal likelihood.</p>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import pylab as plt\n",
      "%matplotlib inline\n",
      "N = 100\n",
      "x = np.sort((10*np.random.rand(N,1)-5),axis=0)\n",
      "t = 5*x**3 - x**2 + x\n",
      "noise_var = 150\n",
      "t = t + np.random.randn(N,1)*np.sqrt(noise_var)\n",
      "plt.plot(x,t,'ro')\n",
      "plt.xlabel('x')\n",
      "plt.ylabel('t')\n",
      "sig_sq = 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1132420d0>"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p>Having generated the data, we fit models of increasing complexity, each time computing the posterior and the marginal likelihood. In the plots we show the model implied by the posterior mean of the parameters.</p>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "test_x = np.arange(-5,5,0.1)[:,None]\n",
      "X = np.ones_like(x);\n",
      "testX = np.ones_like(test_x)\n",
      "max_order = 8\n",
      "log_marg_like = []\n",
      "for i in np.arange(max_order)+1:\n",
      "    prior_mean = np.zeros((i+1,1))\n",
      "    prior_cov = np.eye(i+1)\n",
      "    X = np.hstack((X,x**i))\n",
      "    testX = np.hstack((testX,test_x**i))\n",
      "    posterior_cov = np.linalg.inv((1.0/noise_var)*np.dot(X.T,X) + np.linalg.inv(prior_cov))\n",
      "    posterior_mean = np.dot(posterior_cov,(1.0/noise_var)*np.dot(X.T,t) + np.dot(np.linalg.inv(prior_cov),prior_mean))\n",
      "    plt.figure()\n",
      "    plt.plot(x,t,'ro')\n",
      "    plt.plot(test_x,np.dot(testX,posterior_mean))\n",
      "    plt.title('Model order ' + str(i))\n",
      "    marg_cov = noise_var*np.eye(N) + np.dot(X,np.dot(prior_cov,X.T))\n",
      "    marg_mean = np.dot(X,prior_mean)\n",
      "    this_marg = -((i+1)/2.0)*np.log(2.0*np.pi) - 0.5*np.log(np.linalg.det(marg_cov))\n",
      "    this_marg -= 0.5*np.dot((t-marg_mean).T,np.dot(np.linalg.inv(marg_cov),t-marg_mean))\n",
      "    log_marg_like.append(this_marg)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Fu3DqFDz3nBmIveQSM0D74IOwbx/cc48CvkiqiiTo1wGfAT4H/A8m0ANcCtxg\nXxcDq/D93HgYmAOMsy/FEbx/2stsbQ16PNTa9+7qmwsvNCWW06er+kYknUSS3tnquv0q8DX79nTg\nSeA0cADYC1wJ/BkYCGy3z1sPzADisx1TCmjLygp6PHDte02eEhFHtPp1twAv2LdHAo2uxxqBUUGO\nH7KPSw8VlpdTERC5nRp8J30zfbpJ37z+utI3ItJ1T38rkBvk+ELgF/btCuAUsCGK7aK6urr9dkFB\nAQUFBdF8+ZQQbFVMT0kFP6+7mutma+cpkVRXX19PfX19WM+JtGSzDPgm8LeAk0i+y75eal9vBqow\n6Z0XgQn28RuBKcDcIK+rks0wBFbfzJplgr168yLpJdYlm8XA9zCB2z1y+Dym1/8AJn0zDpPHt4Bm\nTH5/O3AzUBPB+6e8zmrwAydPTZsGP/qRBmNFpHORBP0VQH98A7ovA/OAXcAz9nWbfczpts8D1gI5\nmDEADeKGEKoG/+19g3ir4er2yVOlpfDYY0rfiEj3aEZuglpUVMS9dXUAHGU4G7iJtZRxIHsE5d+7\nQOkbEelAM3KTWEbLGZ5jBusopZ4CpvE8D3In9ZPgnh+8GO/miUiSUtBPMM7G4atf+Rlf4E1ms4bH\nuJmBHAfg1zlFcW6hiCQzBf0E4FTfrKz5C8cOt/C587dQMu7nXPjB75nd1NR+XrS2NRSR9KWcfpwE\nVt9ceXkj5/3pLh57dwN97HHvObm5ZI8cyfCBA3u0Dr6IpBctrZyA3EsXf/rTZuPw66+H+6/zDdy6\nVRYVsTiCbQ1FJH1oIDdBHDvmW/vmww9NmeXvfgef+pTvnHAXTxMR6QkF/Rg5fdq3cbgzeerBB0Pv\nPNXdxdNERCKhoB9l7vTN+PEmfRNq8pS3tpb1lZUcP3CAltZWvtW/P/9x6lT74xq4FZFoU9CPgp4s\nXbyqupr6H/6QcadOsdo+5gWu79+fUZdcwsBRoyjWwK2IRJkGcnsoko3DvbW1rLz+esa1tHBvkMc1\neCsiPaGB3BgITN+UlYW/9k1dTQ0TWlpCPq7BWxGJFQX9bnAvXRyq+iYcma2ttHXyuAZvRSRWtAhv\nCKdOwcaNvo3Dd+yABx6A/fvhBz/oecAHU6lTCBzG7EDjdmduLlM1eCsiMaKefoBg6Zv162HQoOi9\nx+lhw1jXpw+lZ8+yHrObTFtGBueMHcuc5cs1eCsiMaOgj5k8tWGDWegsGumbzqyqruYvP/0ppWfP\nshW4EHhd0fh3AAAJvUlEQVQTGDdzJvdviOqOkyIiHaR99c7tt5tyy+nTTbAvKIjtzlM3nHceT7//\nfofjM4cN46n33ovdG4tIylP1TjfMmQNLl8Z25yn3tod89FHQc7LbOhvaFRGJjrQP+pdfHtvXD9z2\n8IYQ553MTPu/ChHpBareibG6mhqWNDTgBRYBZ4FvBpxzW2Ym+d/+du83TkTSjrqXMZbZ2ooX2AI4\ne179Cfg7YHBWFtaAAeR/+9vMq66OVxNFJI0o6MdYW1YWdZiAvwVY4npsbp8+3LRunUo0RaTXKL0T\nY4Xl5byTnU0d/gEf4JGWFrauWBGPZolImlLQj7H8khIGTJgQ8ieV1tkRkd4UjaD/z5jxyU+4jt0N\nvA3sAQpdx78AvGU/tjwK750UZi5ezO6cnKCPaZ0dEelNkQb9i4CpwJ9dxy7FVCZeChQDq/BNFngY\nmAOMsy/FEb5/UsgvKWHKggXMDQj8Cz0erbMjIr0q0hm5PwUWA/8f04v/ANPLPwvcb5+zGajGfDH8\nGphgH58JFABzg7xuwq+n3xPe2lq2rlhB35MnOZOdzVRtkiIiURTrGbnTgUbM0jFuI4FXXPcbgVHA\nafu245B9PG3kl5QoyItIXHUV9LcCuUGOV2B69O58fVTX8al21a0XFBRQUFAQzZcXEUl69fX11NfX\nh/WcngbqPOBXwP/a9y/E9NyvBGbbx5ba15uBKkx650V86Z0bgSmkUXpHRCSWYpne2Qlc4Lq/H19O\n/3lgA/AAJn0zDtgOWEAz5othO3AzUNPD90847kXV2rKyKCwvVypHRBJOtGbkurvlu4Bn7Os2YJ7r\n8XnAWiAHeAHzKyDpBS6qBlBh31bgF5FEkvbr6UfDoqIi7q2r63C8sqiIxZtT4ntNRJJAd9I7mpEb\nBZmtrUGPa7atiCQaLbjWQ+4c/u6dO4Oeo9m2IpJoFPR7YFV1NW8uW8YjLS0AeIG5mZk84tr9aqHH\nQ7Fm24pIglFOP0ze2lpWXn89T9sBv/04sGrYMMbn5Wm2rYjEhfbIjYG6mhomBAR8gHzg13l5VIc5\nUUJEpDdpIDdMma2thNrCXDl8EUl0CvphOtrcTCFmHQq323JytGKmiCQ8pXfC4K2tpfXw4fb9biuB\nvsDO/v25ZsEC5fBFJOFpIDcMziQsL2Ylur7AGeDwxIms3rEjvo0TkbSngdwocyZh5dsXR/WgQXFp\nj4hIuJTTD0NbVlbQ4xrAFZFkoaAfhsLycio8Hr9j2vJQRJKJcvph0paHIpKoupPTV9DvgtbJF5Fk\noYHcCGmdfBFJNcrpd6KupsYv4AMsaWhg64oVcWqRiEhkFPQ7oXXyRSTVKOh3QiWaIpJqFPQ7oRJN\nEUk1qt7pgko0RSRZqGRTRCSNaGN0ERHxo6AvIpJGIg3684HdwE7gftfxu4G3gT1Aoev4F4C37MeW\nR/jeIiISpkhm5H4RmAZcBpwGhtvHLwVusK9HAb8ExgEW8DAwB9gOvAAUA5sjaIOIiIQhkp7+PwI/\nxAR8gGP29XTgSfv4AWAvcCUwAhiICfgA64EZEby/iIiEKZKe/jjMXiL3ASeB7wL/DYwEXnGd14jp\n8Z+2bzsO2cfjSguqiUg66SrobwVygxyvsJ87FJgMXAE8A4yNVsOqq6vbbxcUFFBQUBCtl26nBdVE\nJJnV19dTX18f1nMiqdP/L2ApsM2+vxfzBXCrfX+pfb0ZqAL+DLwITLCP3whMAeYGee1eqdN39rwN\nVFlUxOLNGmoQkeQS6zr9jcA19u1LgP7Ae8DzwEz7/hhMGmg70AQ0Y/L7GcDN9mvEjRZUE5F0E0lO\n/z/ty1vAKWCWfXwXJtWzC2gD5mEqd7BvrwVyMNU7ce1Oa0E1EUk3ab0MQ7Cc/kKPh+Lly5XTF5Gk\no7V3ukELqolIqlDQFxFJI1pwTURE/Cjoi4ikEQV9EZE0oqAvIpJGFPRFRNKIgr6ISBpR0BcRSSMK\n+iIiaURBX0QkjSjoi4ikEQV9EZE0oqAvIpJGFPRFRNKIgr6ISBpR0BcRSSMK+iIiaURBX0QkjSjo\ni4ikEQV9EZE0oqAvIpJGIgn6k4DtwGvA74ErXI/dDbwN7AEKXce/ALxlP7Y8gvcWEZEeiCToLwMq\ngYnA9+37AJcCN9jXxcAqfLuzPwzMAcbZl+II3j9p1dfXx7sJMZPKnw30+ZJdqn++7ogk6B8GBtu3\nhwCH7NvTgSeB08ABYC9wJTACGIj5dQCwHpgRwfsnrVT+h5fKnw30+ZJdqn++7siM4Ll3Ab8B/g3z\n5XGVfXwk8IrrvEZgFOZLoNF1/JB9XEREeklXQX8rkBvkeAVQbl+eA64H/hOYGtXWiYhIVGV0fUpI\nzcAg1+t8hEn33GUfW2pfbwaqgD8DLwIT7OM3AlOAuUFeey/giaBtIiLpqAH4VKxefAcmaAP8LaaC\nB8wA7utAf2CM3Qjny+VVTH4/A3iBNB3IFRFJRn+FCeKvAy9jqngcCzG99T1Akeu4U7K5F6jpnWaK\niIiIiEhCmQ/sBnYC98e5LbHyz8BZ4BPxbkiU/Svm7+4N4Fl8pb3Jrhjz6/Vt4F/i3JZouwgz5vZH\nzP+58vg2Jyb6YiaT/iLeDYmBIcDPMP/vdgGT49uc8H0RUznUz74/PI5tiZWLMIPc+0m9oD8V3xyQ\npfgG9ZNZX0xacjTm3+Xr+IoSUkEu8Hn79gDgT6TW5wP4J+AJ4Pl4NyQG1gG32LczScKO1jPANfFu\nRIz9FLiM1Az6btcCj8e7EVFwFeZL2nEXvkq1VLQRU6CRKi4EfonpUKZaT38wsK+7JyfqgmvjgHzM\nJK96zKBxKpmOmaj2Zrwb0gtuwVRqJbtRwEHXfWfSYSoajSnMeDXO7YimB4HvYdKpqWYMcAxYg6mq\n/AlwTqiTI5mRG6nOJn5lAkMxeakrMD3/sb3XtKjo7PPdjf9CdJHMl4iXUJ9vIb6eVAVwCtjQW42K\nISveDeglAzC54TuA43FuS7R8BTiKyecXxLcpMZEJXA58G1M6/xDmV+j349mocP0XvjkAYHKpw+LU\nlmjLA45g0jr78a1RdH4c2xQLZcBvgew4tyNaJuOf3rmb1BvM7QdsAb4T74ZE2X2YX2n7MWuGncCs\n/ZUqcjGfzfE3wKY4taXHbgPusW9fArwTx7bEWirm9IsxVSDnxbshUZSJmWg4GjPxMNUGcjMwgfDB\neDckxqaQejl9AC8mVgJUk4QVj/2AxzATuf5Aav4kc+wj9YL+25hlN16zL6vi25yo+TKmqmUvpqef\nSv4Gk+9+Hd/fWyrOmJ9CalbvfA6T2km1MmkRERERERERERERERERERERERERERERERERkcTwf6QZ\nV110d/brAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1131adc90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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dm2AdOGDq6Z99Fv7xD/jv/4aZMyE9HVq3DtvbiiQkBf0E09ACajXJyT4XOqvp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\nRIf/DwCOA5G4SabkAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1131be4d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ixzTSFw/O5Qn+JIKXeISXeIS+vIsl+kumpb3j6+6JyGmUZaRf43RPSnDJsFo5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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x113144710>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bk3iBtmwikhy2cTkjmUjNvKO+7p6IeIHSO+L0RvIaluX+wCk2spbriaFwjXdd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\nEjDUvH0K9Ab+BXT3au9ERMS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       "text": [
        "<matplotlib.figure.Figure at 0x1131d06d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2ibe7JyLlqMhIv0b1dEX8QZbFwrHNO3mWFC5lPedymF9owwheIMr2u7e7JyIe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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1130aaf10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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C5qa/uY0PWcslTGUM/8cHhAFfZnfxdfVExAt0j1wBjE7axx48wOKcb2jLGjbS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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11313b610>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KJ3JFRMLRnzGC+Erga4wqHpeRGKP19YDFo91VsrkRyKmdboqIiIiI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\nAVt6EDNx4kC+AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1135142d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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qN2tGr2eeKa7bVwmiiH8o6EuF/eWSwWyzDaEJu5jECK5kLXDms1tFJDAopy/l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\nI93zlNk2wbxfCIwGfgaWAC3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       "text": [
        "<matplotlib.figure.Figure at 0x1130eca10>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<p>Finally, we can make a bar plot of the (log) marginal likelihood values. Because the first two models are so bad, it's not too easy to see, but the 3rd order model has the highest value. To check this, we can use the `numpy.argmax` method (and add 1, because the third order model is stored in index 2)</p>"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "log_marg_like = np.array(log_marg_like)\n",
      "plt.bar(np.arange(max_order)+1,log_marg_like)\n",
      "print \"Maximum marg likelihood for order \", log_marg_like.argmax()+1\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Maximum marg likelihood for order  3\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x113239c50>"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}